On existence of meromorphic solutions for nonlinear q-difference equation

Abstract

In this paper, we mainly consider the existence of meromorphic solutions of nonlinear q-difference equation of typewhere the right-hand side is irreducible, P(z, f (z)) and Q(z, f (z)) are polynomials in f with rational coefficients, and q is a nonzero complex constant. We obtain that such equation has no transcendental meromorphic solution when |q| = 1 and m = degAnd we investigate the growth of transcendental meromorphic solutions of nonlinear q-difference equation and find lower bounds for their characteristic functions for transcendental meromorphic solutions of such equation for the case |q| ̸ = 1.